Problem: Is ${419108}$ divisible by $4$ ?
Solution: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{4191} {08} = \gray{4191} \gray{00} + {08} $ Because $419100$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${8}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $8$ , divisible by $4$ Yes, ${8 \div 4 = 2}$, so $419108$ must also be divisible by $4$.